I really do not know what else I can do ...
Can anybody help me with that?

What's do you mean with a manual upgrade (only database)?

Using Instalatron to upgrade was the first mistake, actually installing via instalatron was the first mistake.
You best bet is to restore the backup of your forum (certainly database, but perhaps the files also so that you can verify it's in working order).
Then follow https://www.phpbb.com/support/docs/en/3 ... /upgrade3/
I would disable and then delete the styles since they cannot be used in 3.2.x. Make sure all mods are removed completely (especially the database changes). Use the STK (https://www.phpbb.com/support/stk/).

Manual upgrade : for me it was following this procedure: https://www.phpbb.com/support/docs/en/3 ... /upgrade3/
I'm working on forum clone (again Installatron) made especially to train the upgrade procedure.
The problem is, that it can be, that some upgrade via Installatron was tried before and some trashes can be stored in "original" forum.
I will try with the styles.
I've tried STK already - but with first attempt it has deleted all databases
With second try - no change ... - but I've played only with database.
Is there some more detailed description what to check and try using STK?

You mean tables, not databases.
For one, the STK has identified the extra tables correctly, and then proposes to remove them, which is actually the proper action to take, since upgrading should be done on a database without any extras. I take it that "clone" is a kind of backup you wanted to keep, in which case working on the database with the clone/backup is a bad idea. Should anything go wrong while you're working on that database, you might lose your backup.

So, copy that database to somewhere safe (as you backup) and work with the database with only the tables needed for your board ( so let the STK get rid of the bb_"tables" or delete them yourself).

Use original phpBB files which you downloaded from here and follow the upgrade instructions in the document (if you wish to persist in using installatron and something doesn't function as expected - then support is up to the host since they (should) know what their installatron does.

Tables - You are right.
Clone - is actual clone done using Installatron (again ) on subdomain. It allows easily to test things before I will work on source.
In my opinion those tables are used by cloned forum.

config is from the clone because I'm trying to upgrade the clone first.
I've just tried again (working on cloned forum): https://www.phpbb.com/support/docs/en/3 ... /upgrade3/
-restored backups
-run STK database clean without the first step with bb_ tables
- in step 12.4 result is: Invalid scheme name ''

config is from the clone because I'm trying to upgrade the clone first.

As stevemaury said, the STK marked the tables as extra, therefore they are not part of the default phpbb installation in which you have installed the STK.
If you really want to test a copy of your live board, then I suggest either duplicating it in another directory e.g. if your main board is at (public_html)/phpBB/, then make a copy at (public_html)/copy1/ (or something else)? Or make a copy on localhost (personal webserver on your PC).

Clone is done in this way as You've described.
Our hosting gives possibility to create subdomains.
Every used subdomain has it's own directory.
Runing forum and clone are in separated folders. They use also different databases - I see in phpMy Admin.

Clone is done in this way as You've described.
Our hosting gives possibility to create subdomains.
Every used subdomain has it's own directory.
Runing forum and clone are in separated folders. They use also different databases - I see in phpMy Admin.

The STK marked the tables starting with bb_as extra! So in which base or clone phpBB installation is that STK installed?, in other words, which database can it test and clean?

I do not know how to explain it better.
When working on clone - STK, upgrade and so on are runing on clone directory.
During "cloning" - new database is created - copy of original - different name. Tables as I can see - have the same names.
If I choose in STK to delete those 'extra' marked tables - clone crashes.
Take a look to the names of this tables (picture included few posts before) - for me they looks like 'necessary' tables...

One more strange thing - it's looking in '/styles/all/template' folder when after upgrade I do not have in /styles folder called /all